Free Printable Graphing Quadratic Functions

Worksheets

Graphing Quadratic Functions

Total questions: 25

Worksheet time: 2hrs 7mins

Name

Class

Date

Which of the following is correct for the vertex of the parabola

f(x) = 2x² + 8x - 12 ?

There is a local minimum at -2, -20

There is a local maximum at -2, -20

There is a local minimum at 2, 12

There is a local maximum at 2, 12

None of the above

The above shows part of the graph of the function f(x) = x² − 2x − 8

What is the equation of its axis of symmetry?

y = -9

y = 1

x = 2

x = 1

The above shows part of the graph of the function f(x) = x² + 2x − 15

What is the equation of its axis of symmetry?

y = -16

x = -1

x = -2

y = -1

None of the above

Which is the vertex of y = x²+ 16x + 71 ?

V(-8, 7)

V(-8, 3)

V(8, 10)

V(16, -2)

Find the y-intercept of f(x) = 2x²- 2x + 1

(1,0)

(-2,0)

(0,1)

(0, -1)

Does the equation open up or down?
Y = -3x² +7x - 2

down

Neither; it opens to the right.

Neither; it opens to the left.

Given: y = 2(x - 5) + 6, the vertex is

(2, -5)

(-5, 6)

(2, 6)

(5, 6)

A parabola has a vertex at (-3, 2). Where is the axis of symmetry?

y = -2

x = 3

x = -3

y = 2

The parabola shown above has its minimum point at (0.5, -16). What is its equation?

f(x) = -4x² - 4x -15

f(x) = 4x² - 4x -15

f(x) = -4x² + 4x -15

f(x) = -4x2 + 4x -15

10.

A parabola has its maximum point at (-1, 49) The y-intercept is (0, 40)

What is its equation?

f(x) = -9x² + 18x +40

f(x) = 9x² + 18x - 40

f(x) = 9x² - 18x +40

f(x) = -9x2 -18x + 40

11.

Which of the following is a transformation of the graph y = 3x².

Shifts up 3.

Shifts left 3.

Vertical stretch by a factor of 3.

Shifts right 3.

12.

Which of the following is a transformation of the graph y = x² + 4 ?

Shifts left 4.

Shifts right 4.

Shifts up 4.

Shifts down 4.

13.

y = (x - 2)² + 2

y = (x + 2)² + 2

y = (x - 2)² - 2

y = -(x - 2)² + 2

14.

What is the vertex of the function y = (x - 3)² + 5

(-3, 5)

(3, -5)

(-3, -5)

(3, 5)

15.

A parabola has a vertex at (-3, 2). Where is the axis of symmetry?

y = -2

x = 3

x = -3

y = 2

16.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

Maximum

Minimum

Not enough information

17.

The graph of a quadratic function is called a

Parabola

Vertex

Axis of Symmetry

Vertex Form

18.

Which quadratic function is represented by the graph?

y = 2(x - 4)² + 5

y = 2(x + 4)² + 5

y = -2(x - 4)² + 5

y = -2(x + 4)² + 5

19.

Find the y-intercept of the function

y = -3(x + 2)² - 5

(0, -5)

(-2, -5)

(0, -17)

(2, -5)

20.

The equation h=-16t² +47t+3 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked. What is the maximum height the football reaches?

(-1.47,-100.66)

(1.47,37.52)

37.52

-100.66

21.

A rectangular picture measuring 5 inches by 9 inches is surrounded by a frame with uniform width x. Write a quadratic function in standard form to show the combined area of the picture and frame.

f(x) = 4x=28

f(x) = 8x+28

f(x) = 4x²+28x+45

f(x) = x²+14x+45

22.

Rewrite the equation in vertex form
y = -2x² +8x-6

y = 2(x+2)²-2

y = -2(x-2)²+2

y = -2(x-2)²-2

y = 2(x-2)²+2

23.

Find the zeros of the function f(x) = x²+13x+30

(x+3)(x+10)

x = -3 and x= -10

(x-3)(x-10)

x= 3 and x=10

24.

Find the roots of the equation 32x-64=4x²

(x-16)(x-16)

x=16

x= 4 and x= -4

x = 4

25.

Does
y = -4x²
have a maximum or minimum value?

maximum

minimum

Reset

Graphing Quadratic Functions

Total questions: 25

Worksheet time: 2hrs 7mins

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